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Question
A body of mass 0.5 kg travels in a straight line with velocity v = a x3/2 where a = 5 m–1/2s–1. The work done by the net force during its displacement from x = 0 to x = 2 m is ______.
Options
1.5 J
50 J
10 J
100 J
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Solution
A body of mass 0.5 kg travels in a straight line with velocity v = ax3/2 where a = 5 m–1/2s–1. The work done by the net force during its displacement from x = 0 to x = 2 m is 50 J.
Explanation:
Given, v = ax3/2
m = 0.5 kg, a = 5 m–1/2s–1, work done (W) = ?
We know that
Acceleration `a_0 = (dv)/(dt)` = `v (dv)/(dx) = ax^(3/2) d/(dx) (ax^(3/2))`
= `ax^(3/2) xx a xx 3/2 xx x^(1/2)`
= `3/2 a^2x^2`
Now, Force = `ma_0 = m 3/2 a^2x^2`
Work done = `int_(x = 0)^(x = 2) Fdx`
= `int_0^2 3/2 ma^2x^2dx`
= `3/2 ma^2 xx (x^3/3)_0^2`
= `1/2 ma^2 xx 8`
= `1/2 xx (0.5) xx (25) xx 8`
= 50 J
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